Entropy of semiclassical measures in dimension 2

Abstract

We study the asymptotic properties of eigenfunctions of the Laplacian in the case of a compact Riemannian surface of Anosov type. We show that the Kolmogorov-Sinai entropy of a semiclassical measure for the geodesic flow is bounded from below by half of the Ruelle upper bound

42 pages, 3 figures. Compared to the second version, I have removed the proof in the case of surfaces of nonpositive curvature and I have written it in a different article (arXiv:0911.1840)

References in corpus (2)

• Entropy of semiclassical measures of the Walsh-quantized baker's map
• Entropic bounds on semiclassical measures for quantized one-dimensional maps

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• Joint Quasimodes, Positive Entropy, and Quantum Unique Ergodicity
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